Tag Archives: TFMTCNE

If you were an alien who had learnt everything you know about Earth from watching TV and movies you would probably think that the sole purpose of a car’s petrol tank is to explode.

It doesn’t take much to cause a movie petrol tank to explode: a serious crash, a well-placed gunshot or even a lightning strike1 will do it; and driving the car off a cliff makes it an absolute certainty.

Reality is far more boring. Petrol tanks are specifically designed with safety in mind: most are produced from tough plastic (HDPE to be exact) and have built-in features that ensure that the mixture of liquid fuel, fuel vapour and air never reaches the flammability limit (petrol must be between 1.4% and 7.6% (by volume) in air in order for it to catch fire). Petrol does not usually detonate as explosives do, but rather it deflagrates, burning subsonically (below the speed of sound) and therefore not creating a shock wave.

In certain circumstances petrol can explode, especially if trapped in a sealed container (petrol tanks have relief valves to prevent this) which can create a BLEVE (pronounced “blevvy”) which stands for Boiling Liquid Expanding Vapour Explosion2 in which a sudden change in pressure inside the tank causes the liquid fuel to turn into vapour, causing the container to explode and releasing a cloud of vapour that can then ignite, causing a (usually larger) secondary explosion.

The Magical Shotgun (and it’s close cousin, The Magical Pistol) is a staple of the over-the-top action movie. The Magical Shotgun will be familiar to anyone who’ve ever watched a John Woo film: a character hit by a shotgun blast is thrown backwards at great speed through the air, usually into a plate glass window.

Unfortunately this just isn’t possible and the Law of the Conservation of Momentum explains why: in any collision, whether it’s a car striking a bus, or buckshot striking our leading man, momentum must be conserved. The total momentum before the collision must equal the total momentum after the collision.

Momentum is the product of mass and speed and can be loosely thought of as indicating how difficult it would be to change the motion of something. The graph below shows how momentum changes – a darker background indicates greater momentum.

The momentum before the collision is the mass of the shot multiplied by its speed: using typical values of 30 grams of shot travelling at 350 metres per second we have a momentum of 10.5 kgm/s. After the collision the momentum is the combined mass of the target plus the shot, multiplied by the speed of the target moving backwards.

If we assume the target is an average-sized man with a mass of 85 kg and that he’s standing still before he gets shot then the combined mass is 85.03 kg, which, with a momentum of 10.5 kgm/s gives us a final speed of 0.12 m/s or twelve centimetres per second (0.27 mph); this bears no relation to what’s seen on film.

The grapple gun is a staple of the action movie genre: simply point the hook skywards, fire and have the gun lift you onto the roof of your local Abandoned Warehouse™ or Deserted Chemical Plant™. The Batman is particularly fond of the Grapple Gun, making it a staple of his famous Utility Belt.

So let’s look at the physics:

Assuming The Batman is a well-built adult male and that he’s wearing a substantial amount of body armour and equipment, a mass of 150kg is probably reasonable. Raising a 150kg weight to the top of a ten storey (30m) building requires about 45,000 joules of energy (45 kJ). If The Batman takes thirty seconds to do the journey then that is equivalent to a power of 1500 W. A motor capable of lifting The Batman’s 150 kg weight is probably about 75% efficient, meaning the motor has to develop about 2000 W.

If we assume that the grapple gun’s motor is no more than 5 kg in mass (for ease of wielding) that gives a power-to-weight ratio* of 400 W/kg. This is within the capabilities of modern electric motors, but only just. Finding a battery that can provide 45 kJ is not difficult; lithium ion batteries can provide about 600 kJ per kilogram. However, they can’t supply that electricity quickly enough, managing only about 300 W/kg which means that the Grapple Gun’s 5 kg motor is going to come with a substantial 5kg battery to match. Then there’s the weight of the gun itself and the super-strong cable to consider …

Whilst devices for firing grappling hooks do exist (I’m told the Battelle Tactical Air Initiated Launch system is good) and powerful electric motors are fairly common, merging the two to create a useful handheld device is beyond the capabilities of physics at the moment. A real grapple gun would be far too bulky, heavy and unwieldy to be of any practical use.

* Of course this should really be power-to-mass ratio, but I’m going to stick with the more commonly used term.